Exploiting orbits in symmetric ILP

Margot, François

doi:10.1007/s10107-003-0394-6

Cited by 118 publications

(111 citation statements)

References 29 publications

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“…The existence of symmetry in the model, which implies many alternative solutions with the same objective value, decreases branch and bound efficiency since many nodes with equivalent solutions are explored, which significantly increases the computational time (Margot, 2003). This also explains why unbalanced cases are easier to solve, since they may have less symmetry.…”

Section: Discussionmentioning

confidence: 99%

Computational strategies for large-scale MILP transshipment models for heat exchanger network synthesis

Yang

Grossmann

Miller

2015

Computers & Chemical Engineering

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Determining the minimum number of units is an important step in heat exchanger network synthesis (HENS). The MILP transshipment model (Papoulias and Grossmann, 1983) and transportation model (Cerda and Westerberg, 1983b) were developed for this purpose. However, they are computationally expensive when solving for large-scale problems. Several approaches are studied in this paper to enable the fast solution of large-scale MILP transshipment models. Model reformulation techniques are developed for tighter formulations with reduced LP relaxation gaps. Solution strategies are also proposed for improving the efficiency of the branch and bound method. Both approaches aim at finding the exact global optimal solution with reduced solution times. Several approximation approaches are also developed for finding good approximate solutions in relatively short times. Case study results show that the MILP transshipment model can be solved for relatively large-scale problems in reasonable times by applying the approaches proposed in this paper. • Several approximation approaches are developed for finding near optimal solutions. Key Words• Some relatively large-scale MILP transshipment models are solved in reasonable times by using the approaches proposed in this study.

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Section: Discussionmentioning

confidence: 99%

Computational strategies for large-scale MILP transshipment models for heat exchanger network synthesis

Yang

Grossmann

Miller

2015

Computers & Chemical Engineering

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“…This section extends the material in [61,62] to 0-1 MINLPs. Consider a formulation P in the form (1) where X = {0, 1} n and a constraint set C(P ) which we suppose in the form g(x) ≥ b ∈ R m .…”

Section: The Symmetry Group Narrowingmentioning

confidence: 92%

“…The symmetry group G is used in [61,62] to derive techniques that help the BB algorithm avoid taking symmetric optima into consideration. Let I n = {1, .…”

Section: The Symmetry Group Narrowingmentioning

confidence: 99%

Reformulations in Mathematical Programming: Definitions and Systematics

Liberti

2009

RAIRO-Oper. Res.

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Abstract. A reformulation of a mathematical program is a formulation which shares some properties with, but is in some sense better than, the original program. Reformulations are important with respect to the choice and efficiency of the solution algorithms; furthermore, it is desirable that reformulations can be carried out automatically. Reformulation techniques are very common in mathematical programming but interestingly they have never been studied under a common framework. This paper attempts to move some steps in this direction. We define a framework for storing and manipulating mathematical programming formulations, give several fundamental definitions categorizing reformulations in essentially four types (opt-reformulations, narrowings, relaxations and approximations). We establish some theoretical results and give reformulation examples for each type. Keywords

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“…Since then, many articles discuss how to detect and exploit syntactic symmetries in SAT solving [7,5,8,9,10,11,12,13,14]. Symmetries have been also extensively investigated and successfully exploited in other domains besides SAT like Constraint Satisfaction Problem [15,16], Integer Programming [17,18], Planning [19,20], Model Checking [21,22,23,24], Quantified Boolean Formulas (QBF) [25,26,27], and Satisfiability Modulo Theories (SMT) [28,29,30].…”

Section: Symmetries In Automated Theorem Provingmentioning

confidence: 99%

Symmetries in Modal Logics

Areces

Hoffmann

Orbe

2013

Electron. Proc. Theor. Comput. Sci.

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In this paper we develop the theoretical foundations to exploit symmetries in modal logics. We generalize the notion of symmetries of propositional formulas in conjunctive normal form to modal formulas using the framework provided by coinductive modal models introduced in [1]. Hence, the results apply to a wide class of modal logics including, for example, hybrid logics. We present two graph constructions that enable the reduction of symmetry detection in modal formulas to the graph automorphism detection problem, and we evaluate the graph constructions on modal benchmarks.

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Exploiting orbits in symmetric ILP

Cited by 118 publications

References 29 publications

Computational strategies for large-scale MILP transshipment models for heat exchanger network synthesis

Computational strategies for large-scale MILP transshipment models for heat exchanger network synthesis

Reformulations in Mathematical Programming: Definitions and Systematics

Symmetries in Modal Logics

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